To enrich a flow of air with oxygen, the production of high-purity oxygen is not required and the use of a distillation device containing a mixing column as described in document U.S. Pat. No. 4,022,0310 (Brugerolle) is suitable. Combined plants of a blast furnace and an air distillation device which comprises such a mixing column are described, for example, in the documents U.S. Pat. No. 5,244,489 (Grenier) and EP-A-0,531,182, in the name of the Applicant. However, the approaches followed in these two documents are at variance: in document U.S. Pat. No. 5,244,489, the distillation device is entirely fed with air via a diversion of the blast from a blast furnace blowing engine and the part of the flow of air supplied to the mixing column is given a slight positive pressure by means of a blower driven by a cold-temperature-maintenance turbine which depressurizes the part of the flow of air directed to the medium-pressure column, in an arrangement which makes it necessary, in order to achieve the said positive pressure, to turbine a large part of the air fed to the medium-pressure column, giving rise to losses of extraction yield and of energy, as well as oversizing of the stations for refrigerating and purifying the air fed to the distillation device. In contrast, document EP-A-0,531,182 envisages a complete separation of the air supplies a) for the blast furnace, b) for the medium-pressure column and c) for the mixing column, using separate compression means in order, in particular, to allow the production, in the mixing column, of impure oxygen at high or low pressures, in an arrangement which is expensive in terms of the investment in and running of rotating machines and which does not envisage any synergy between these machines.